Efficient and scalable quantum algorithms for ground-state preparation

Design efficient and scalable quantum algorithms for ground-state preparation of general Hamiltonians, addressing the unresolved algorithmic and implementation challenges associated with quantum imaginary-time evolution and related approaches.

Background

The paper places quantum ground-state preparation in the context of computationally difficult problems, noting that general ground-state preparation is both NP-hard and QMA-complete. Existing quantum imaginary-time-evolution methods face scalability and hardware constraints, including rapidly increasing circuit depth and implementation complexity.

The proposed quantum conjugate gradient descent method improves convergence per iteration for the tested Heisenberg-chain instances, but it does not resolve the broader challenge of designing efficient and scalable ground-state-preparation algorithms for general Hamiltonians. The authors therefore identify this as an explicitly unresolved problem motivating further algorithmic development.